will the archive still be associated with the mailbox?
For it to be automatic, it can read the non inherited permissions from AD and also Delegate users set through outlook, but that needs to be associated with a mailbox for that archive.

Otherwise you can either go through the Vault Admin Console and manually assign a windows user Read/Write/Delete access to the archive or you can do it through EVPM, but you may find that things such as Virtual Vault do not work correctly due to extra permissions it can only get from the mailbox itself

If the mailbox doesn't move you must be somehow adding permissions from the users new Domain to their existing mailbox in which case as long as the policy is set correctly when the archive is sync'd this new permissions will filter down to their archive. Then as long as you set a DNS Alias in this new domain to point back to the EV server it will be seemless to the user